'I am doing' = the present...
All three terms are used, aren't they? 'Continuous' is still the most common term I hear and read and 'durative' is fairly rare.
I was originally taught to say progressive, but the term continuous has gradually replaced it. Okay with me, it's just a term.
I learnt them the opposite way- must be a sign of age.
I've never encountered durative before. It sounds pedantic. I think there's a difference between continuous (I am living) and progressive (I am cooking). The former indicates inaction, if you will; the latter indicates action.